Matrix Operations

Front

What is matrix addition?

Back

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. If matrices A and B are both m x n, then A + B is also m x n.

Front

What is the condition for matrix addition to be possible?

Back

Two matrices can be added only if they have the same dimensions (same number of rows and columns).

Front

What is matrix multiplication?

Back

Matrix multiplication involves taking the dot product of rows and columns from two matrices. The resulting matrix has dimensions based on the outer dimensions of the two matrices.

Front

What is the condition for matrix multiplication to be possible?

Back

The number of columns in the first matrix must equal the number of rows in the second matrix.

Front

What is the result of adding the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

A + B = [[1+5, 2+6], [3+7, 4+8]] = [[6, 8], [10, 12]]

Front

What is the result of multiplying the matrices A = [[1, 2], [3, 4]] and B = [[5, 6], [7, 8]]?

Back

A * B = [[1*5 + 2*7, 1*6 + 2*8], [3*5 + 4*7, 3*6 + 4*8]] = [[19, 22], [43, 50]]

Front

What does it mean for two matrices to be compatible for addition?

Back

Two matrices are compatible for addition if they have the same dimensions.

Front

What does it mean for two matrices to be compatible for multiplication?

Back

Two matrices are compatible for multiplication if the number of columns in the first matrix equals the number of rows in the second matrix.

Front

If A is a 2x3 matrix and B is a 3x2 matrix, what is the size of the product AB?

Back

The product AB will be a 2x2 matrix.

Front

Can you multiply a 3x2 matrix by a 2x3 matrix?

Back

Yes, the product will be a 3x3 matrix.